Anahita Ayasoufi

Solution of Radiative Boundary Design Problems Using a Combined Optimization Technique

In this work, a novel combined strategy has been developed and verified for radiative boundary design problems. It is highly efficient and simple to implement and appears promising for obtaining appropriate results in practical applications. In the proposed approach, the determination of the unknown profile of heat flux through active constraints includes utilizing a new search optimization technique that is merged with the maximum entropy method (MEM). It is shown that use of the merged MEM algorithm minimizes both the occurrence of negative values for physically non-negative components, and the oscillatory profile of heat flux. A generalized computational grid based on finite-volume scheme is devised to solve the radiative transfer equation and sensitivity equations. Numerical simulations are conducted to evaluate the performance and accuracy of the present approach with regard to the classical methods involved in its derivation.

Stefan Number-Insensitive Numerical Simulation of the Enthalpy Method for Stefan Problems Using the Space-Time CE/SE Method

An improvement is introduced to the conservation element and solution element (CE/SE) phase-change scheme presented previously. The improvement addresses a well-known weakness in numerical simulations of the enthalpy method when the Stefan number (the ratio of sensible to latent heat) is small (less than 0.1). Behavior of the improved scheme, at the limit of small Stefan numbers, is studied and compared with that of the original scheme. It is shown that high dissipative errors, associated with small Stefan numbers, do not occur using the new scheme.

NUMERICAL SIMULATION AND MIXING STUDY OF NON-NEWTONIAN FLUIDS IN AN INDUSTRIAL HELICAL STATIC MIXER

Static mixers are increasingly being used to perform a variety of mixing tasks in industries, ranging from simple blending to complex multi-phase reaction systems. Use of static mixers to process non-Newtonian fluids is quite common. Data on the pressure drop of non-Newtonian fluids in static mixers and the degree of mixing of materials through the mixer are very useful in the design and engineering application of these tools. This paper extends a previous study by the authors on an industrial helical static mixer and illustrates how static mixing processes of single-phase viscous liquids can be simulated numerically. A further aim is to provide an improved understanding of the flow pattern of non-Newtonian single-phase liquids through the mixer. A three-dimensional finite volume simulation is used to study the performance of the mixer. The non-Newtonian fluid is modeled by the Carreau law model for the shear stress. The effects of the Reynolds number of the flow and also properties of non-Newtonian fluids on the static mixer performance have been studied. The flow velocities, pressure drops, etc. are calculated for various flow rates. The computed pressure drop is in good agreement with existing experimental data. A comparison of the mixer performance for both Newtonian and non-Newtonian fluids is presented. It is shown that for low Reynolds number flows, the fluid type is less effective on the degree of mixing, while as flow Reynolds number increases and the viscosity decreases, it manifests more influence on the downstream mixing. It is also shown that the fluid type has a major impact on the pressure drop across the mixer.Copyright

STEFAN NUMBER-INSENSITIVE NUMERICAL SIMULATION OF THE ENTHALPY METHOD FOR STEFAN PROBLEMS USING THE SPACE-TIME CONSERVATION ELEMENT AND SOLUTION ELEMENT METHOD

An improvement is introduced to the conservation element and solution element (CE/SE) phase change scheme presented previously. The improvement addresses a well known weakness in numerical simulations of the enthalpy method when the Stefan number, (the ratio of sensible to latent heat) is small (less than 0.1). Behavior of the improved scheme, at the limit of small Stefan numbers, is studied and compared with that of the original scheme. It is shown that high dissipative errors, associated with small Stefan numbers, do not occur using the new scheme.Copyright

Application of the Conservation Element and Solution Element Method in Numerical Modeling of Three-Dimensional Heat Conduction With Melting and/or Freezing

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used to solve three-dimensional phase change problems. Several isothermal phase change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate, robust and efficient for the numerical modeling of phase change problems.Copyright

Enhancement of Convective Heat Transfer in Internal Viscous Flows by Inserting Motionless Mixers

In chemical processing industries, heating, cooling and other thermal processing of viscous fluids are an integral part of the unit operations. Enhancement of the natural and forced convection heat transfer rates has been the subject of numerous academic and industrial studies. Motionless mixers, also known as static mixers, are often used in continuous mixing, heat transfer, and chemical reactions applications. These mixers have low maintenance and operating costs, low space requirements, and have no moving parts. Heat exchangers equipped with mixing elements are especially well suited for heating or cooling highly viscous fluids. Shell and tube heat exchangers incorporate static mixing elements in the tubes to produce a heat transfer rate significantly higher than that of conventional heat exchangers. The mixing elements continuously create a new interface between the working fluid and tube wall, thereby producing a uniform heat history in the fluid. It is desired to employ motionless mixers in heat transfer applications to provide a high rate of heat transfer from a thermally homogenous fluid with low pressure drop. In the past, laboratory experimentation has been a fundamental part of the design process of a new static mixer for a given application as well as the selection of an existing static mixer. It is possible to use powerful computational fluid dynamics (CFD) tools to study the performance of these mixers without resorting to experimentation. In this paper, which is an extension to the previous work of the authors, the enhancement of performance of shell and tube heat exchangers by inserting motionless mixers (SMX and helical) is studied for creeping, laminar, and low-Re turbulent flows. It is shown that the studied mixers produced similar flow histories for the working fluid considered. Both SMX and helical mixers are able to increase thermal performance of heat exchangers. The SMX mixer manifests a higher performance in temperature blending and in heat transfer enhancement compared to the helical mixer. However, the pressure drop created by SMX elements, and consequently the required energy to maintain the flow in tube, is significantly higher.Copyright

Large-Eddy Turbulent Flow Simulation of a KOMAX Static Mixer

Viscous liquids have to be homogenized in continuous operations in many branches of processing industries; and therefore, fluid mixing plays a critical role in the success or failure of many industrial processes. Consequences of improper mixing include non-reproducible processing conditions and lowered product quality, resulting in the need for more elaborate downstream processes and increased costs. The range of practical flow Reynolds numbers for KOMAX static mixers in industry is usually from moderate values (Re ≈ 0) to very large values (e.g. Re ≈ 5,000,000). However, most of industrial applicants have a very small flow to moderate Reynolds numbers (e.g. Re ≈ 5,000). This paper presents an improved understanding of the turbulent flow pattern for single-phase liquids through the mixer. Large-Eddy Simulation (LES) model is applied to the flow in a KOMAX static mixer to calculate the flow velocities, pressure drops, etc. Using a variety of predictive tools, the mixing results are obtained.Copyright

Large-Eddy Turbulent Flow Simulation of an Industrial Helical Static Mixer

Viscous liquids have to be homogenized in continuous operations in many branches of processing industries; and therefore, fluid mixing plays a critical role in the success or failure of many industrial processes. Consequences of improper mixing include non-reproducible processing conditions and lowered product quality, resulting in the need for more elaborate downstream purification processes and increased waste disposal costs. The range of practical flow Reynolds numbers for helical static mixers in industry is usually from very small (Re ≈ 0) to moderate values (e.g. Re = 5,000). However, it has been found that the flow regime within helical static mixers is turbulent for relatively low Reynolds numbers, compared to the flow inside a pipe with no mixing elements present. This paper extends previous studies by the authors on the industrial helical static mixer. Its purpose is to present an improved understanding of the turbulent flow pattern for single-phase liquids through the mixer. Three-dimensional finite volume simulations are used to study the performance of the mixer using different turbulent models. Large-Eddy Simulation (LES) model is applied to the flow in an industrial helical static mixer to calculate the flow velocities, pressure drops, etc. Using a variety of predictive tools, the mixing results are obtained. Also, the accuracy and global performance of several different turbulent models are compared against the LES model.Copyright

Three-Dimensional Numerical Simulation and Performance Study of an Industrial Static Mixer Using Pseudo-Plastic Fluids

Mixing is an essential component of nearly all industrial chemical processes, ranging from simple blending to complex multi-phase reaction systems for which the reaction rate, the yield and the selectivity are highly dependent upon the mixing performance. Consequences of improper mixing include nonreproducible processing conditions and lowered product quality, resulting in the need for more elaborate downstream purification processes and increased waste disposal costs. A wide range of working fluids in industrial mixers are non-Newtonian. The non-Newtonian fluid studied here is a member of the pseudo-plastic fluids group, characterized by a progressively decreasing slope or shear stress versus shear rate. These fluids are termed shear thinning; the viscosity decreases with increasing velocity gradient. In this paper, a previous study by the authors on an industrial helical static mixer is extended to illustrate how static mixing processes of single-phase pseudo-plastic liquids can be simulated numerically. A further aim is to provide an improved understanding of the flow pattern of pseudo-plastic single-phase liquids through the mixer. A three-dimensional finite volume simulation is used to study the performance of the mixer. A commercial software, FLUENT, is used in a part of the numerical simulation. The flow velocities, pressure drops, etc. are calculated for various flow rates, using the Carreau and the power law models for non-Newtonian fluids. The numerical predictions by these two models are compared to existing experimental data. Also, a comparison of the mixer performance for both Newtonian and pseudo-plastic fluids is presented.Copyright

A Study of the Accuracy, Global Performance, and Computational Expenses of k–ε, k–ω, and RSM Turbulent Models for Flow in an Industrial Static Mixer

Viscous liquids have to be homogenized in continuous operations in many branches of processing industries; and therefore, fluid mixing plays a critical role in the success or failure of many industrial processes. The use of static mixers has been utilized over a wide range of applications such as continuous mixing, blending, heat and mass transfer processes, chemical reactions, etc. Consequences of improper mixing include non-reproducible processing conditions and lowered product quality, resulting in the need for more elaborate downstream purification processes and increased waste disposal costs. This paper extends previous studies by the authors on an industrial helical static mixer and illustrates how static mixing processes of single-phase viscous liquids can be simulated numerically. It also intends to present an improved understanding of the turbulent flow pattern for single-phase liquids through the mixer. Three-dimensional finite volume simulations are used to study the performance of the mixer for a range of practical Reynolds numbers, using three different turbulent models: k–e model, k–ω model, and RSM model. The accuracy, global performance and costs of the different turbulent models have been examined. The flow velocities, pressure drops, etc. are calculated for each model. The calculated pressure drop of each case is compared with experimental results. Using different tools, the mixing results obtained from the different models are studied and compared.Copyright